We propose to demonstrate the feasibility of a new, simplified approach to multichannel SQUID design. The key innovation is the use of multiplexing to connect several gradiometer coils to a single SQUID sensor. This approach can potentially reduce cost and complexity with little compromise on performance. The primary requirement is the development of a superconducting switch to perform the multiplexing. We propose to use a magnetic field-modulated Josephson junction for this purpose. Using thin-film technology, this device can be fabricated with suitable design parameters for low signal applications. The feasibility of this approach will be validated by converting a commercial single channel SQUID magnetometer into a multiplexed three-channel instrument.